Journal of Mathematical Modeling
Volume:2 Issue: 2, Winter 2014

Consider the following consistent Sylvester tensor equation
X×1A×2B×3C=D,
where the matrices A,B,C and the tensor D are given and X is the unknown tensor. The current paper concerns with examining a simple and neat framework for accelerating the speed of convergence of the gradient-based iterative algorithm and its modified version for solving the mentioned Sylvester tensor equation without setting the restriction of the existence of a unique solution. Numerical experiments are reported which confirm the validity of the presented results.

This work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations AX=B and XC=D with orthogonal constraint. By optimal correction approach, a general representation of the orthogonal solution is obtained. This method is tested on two examples to show that the optimal correction is eective and highly accurate.

In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modi ed Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional problems.

In this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. Tractability and dierentiability index are introduced based on the-smoothing property of a Volterra integral operator and index reduction procedure, respectively. Using the notion of index, we give sucient conditions for the existence and uniqueness of the solutions for the index-3 system. Then, a numerical technique based on the Chebyshev polynomial collocation methods including the matrix-vector multiplication representation is proposed for the solution of these systems and the performance of the numerical scheme is illustrated by means of some test problems.

In this paper, an iterative method is proposed for solving matrix equation ∑sj=1AjXjBj=E. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are de ned. It is proved that the new iterative method obtains the least norm solution of the mentioned matrix equation within finite iteration steps in the exact arithmetic, when the above matrix equation is consistent. Moreover, the optimal approximate solution (X∗1,X∗2,…,X∗s) to a given multiple matrices (X¯1,X¯2,…,X¯s) can be derived by nding the least norm solution of a new matrix equation. Finally, some numerical experiments are given to illustrate the eciency of the new method.

This article presents a perishable (s; S) inventory system under continuous review at a service facility in which a waiting hall for customers is of nite size M. The arrival instants of customers to the service station constitutes a Poisson process. The life time of each items is assumed to be exponential. All arriving customers demand the rst "essential" service, whereas only some of them demand the second "optional" service, and the second service is multi-optional. The joint probability distribution of the number of customers in the waiting hall and the inventory level is obtained for the steady state case. Some important system performance measures in the steady state are derived, and the long-run total expected cost rate is also calculated. We have derived the Laplace-Stieljes transforms of waiting time distribution of customers in the waiting hall. The results are illustrated numerically.

In the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. Then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.